Ascertaining hydraulic fracture effectiveness in the oil & gas industry depends in part on the evaluation of completion quality (e.g., rock susceptibility to fracturing, fracture vertical containment, fracture conductivity, interference of complex natural fracture network, rock-fluid interaction, etc.). Many of the factors indicative of completion quality are influenced to various extents by the mechanical behavior of the source rock in a subsurface formation. The mechanical behavior of geologic materials such as soils and rocks is generally dependent on the applied state of stress and the structure, with the latter generally resulting from the combined effect of fabric (i.e., spatial arrangements of solid particles) and bonding (i.e., links between solid particles).
Geologic materials exhibiting different properties along different locations within their body are generally referred to as heterogeneous. Their heterogeneity may be random or organized. Layered media are examples of materials with organized heterogeneity that exhibit similar properties within a bed plane and different properties perpendicular to the bed plane. These types of materials may be modeled by assuming rotational symmetry in material properties, with an axis of rotation perpendicular to bedding. Because of the laminated structure (which may be fine-scale, as in shales, or large-scale, as in reservoir interbeds) their stress-strain relationships change with orientation to bedding. In general, laminated materials tend to be stiffer along the direction parallel to bedding and more compliant along the direction perpendicular to bedding. Correspondingly, propagating sound waves (compressional and shear) in these materials result in wave velocities that are higher parallel to bedding and lower perpendicular to bedding. The theory of elastic anisotropy describes this behavior. By defining material properties along principal directions of material symmetry, it provides a methodology for predicting material behavior under any conditions of applied loading and deformation.
Geologic materials are complex and often exhibit various types of heterogeneity (e.g., fine-scale texture superposed to the presence of fracture sets and as part of a larger scale structure). Furthermore, the layering may not be ideal (e.g., some beds may have different orientations or be discontinuous). The resulting stress-strain behavior may or may not be well represented by the elastic anisotropic theory, and may change with scale (from sample-scale to log-scale). Furthermore, their stress-strain behavior may not be elastic (e.g., plastic shales).
There are three basic types of formations: formations that have identical elastic properties in all three spatial directions are called isotropic, formations that have identical elastic properties in two directions but a different property in the third direction are called transverse isotropic (TI), and formations that have different properties in all three dimensions are called orthotropic. There are two independent elastic constants, or moduli, that characterize isotropic formations, five independent elastic constants that characterize TI formations and nine independent elastic constants that characterize orthorhombic formations. The aforementioned types of isotropic formations may be modeled using isotropic earth models. For example, to model a TI formation, the five elastic constants associated with TI formations may be determined by a combination of measurements and assumptions, e.g., using data collected by a sonic tool, referred to herein as sonic measurement data, to provide three of the five elastic constants associated with TI formations, with the remaining elastic constants determined via modeling.
Anisotropic formations such as TI formations present challenges in the determination of the stresses and mechanical properties (e.g., properties such as vertical Young's Modulus, horizontal Young's Modulus, vertical plane shear modulus, horizontal plane shear modulus, vertical Poisson Ratio, etc.) that define the mechanical behavior of a subsurface formation. A multitude of approaches and simulation models have been developed, each having different advantages and disadvantages in different scenarios, as well as requiring different measurement data as input. As a result, it has been found that determining stresses and/or mechanical properties for use in evaluating completion quality or in other applications in such environments can be challenging, particularly in the presence of incomplete measurement data and the availability of multiple simulation models and/or approaches.